Three-dimensional surfaces are often represented in computer memory by a contiguous collection of tiles, such as triangular tiles. Such a representation may be referred to as a “tesselation” or a “mesh.”
A “geodesic distance” between two points that lie on a surface is the length of the shortest path, along the surface, that connects the two points. For points lying on a curved surface, this distance is often different from the Euclidean distance between the points. For example, the geodesic distance between two hilltops is the length of the shortest path that runs, along the surface of the Earth, between the two hilltops. This distance is larger than the Euclidean distance between the hilltops, which is the length of a straight path, through the air, passing between the hilltops.
U.S. Pat. No. 4,974,598, whose disclosure is incorporated herein by reference, describes a system and method in medical non-invasive electrocardiographic analysis of human heart beats for the early detection of certain heart diseases in which a large number of electrodes, for example, 32 to 64, are attached on the chest, back and sides of the patient, i.e., “body surface.” The electrical signals detected by the electrodes are converted to digital data, treated to remove muscle artifact and other noise, and then analyzed mathematically to determine the presence or absence of abnormal body surface potential distributions, or of unusual beat morphologies, compared statistically to the self-norm “typical beat” of the patient and also compared to a data base compiled from comparable normal population groups. The results of the statistical analysis are displayed as topographical maps of the body surface, color coded to represent the presence of significant derivations from the norms, defined as “abnormality”, i.e., abnormal spatio-temporal patterns of voltages on the body surface, or as waveshape or histogram displays of features, similarly Z-transformed and color coded. Discriminant functions, stored in the heart state analyzer, estimate the relative probability of various cardiac pathologies.
US Patent Application Publication 2007/0232949, whose disclosure is incorporated herein by reference, describes a method for diagnosing and mapping atrial fibrillation that correlates recordings of electrical activity from intracardiac multi-electrode catheters with the locations of electrodes within the heart to obtain a global mapping of cardiac electrical activity. Time delay and/or amplitude information in the recorded electrical activities is fused with electrode location information to generate a display on a 3-D anatomical template of the heart. Time delay and/or amplitude information is displayed using color code and/or lines of equal value, to aid diagnosis and localization of electrical activity irregularities. Mapping of atrial fibrillation enables physicians to treat arrhythmia by ablation, pacing, shock therapy and/or drugs at initiation or during an episode based on therapy delivery at critical mapped locations for arrhythmia onset or maintenance. Locations for placement of pacing leads and pacemaker timing parameters may also be obtained from the display.
U.S. Pat. No. 8,155,400, whose disclosure is incorporated herein by reference, describes a method of cropping a representation of a face for electronic processing, said method comprising: selecting a first geodesic contour about an invariant reference point on said face, setting a region within said first geodesic contour as a first mask, selecting a second geodesic contour about a boundary of said identified first region, setting a region within said second geodesic contour as a second mask, and forming a final mask from a union of said first mask and said second mask.